scholarly journals Relative dielectric constants and selectivity ratios in open ionic channels

2017 ◽  
Vol 5 (1) ◽  
pp. 125-137 ◽  
Author(s):  
Bob Eisenberg ◽  
Weishi Liu
Keyword(s):  
Ion Channels ◽  
Mathematical Analysis ◽  
Applied Mathematics ◽  
Ionic Channels ◽  
Dielectric Constants ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problems ◽  
Dielectric Coefficient ◽  
Ion Species ◽  
Crucial Parameter

Abstract We investigate the effects of the relative dielectric coefficient on ionic flows in open ion channels, using mathematical analysis of reasonably general Poisson-Nernst-Planck type models that can include the finite sizes of ions. The value of the relative dielectric coefficient is of course a crucial parameter for ionic behavior in general. Using the powerful theory of singularly perturbed problems in applied mathematics, we show that some properties of open channels are quite insensitive to variation in the relative dielectric coefficient, thereby explaining such effects seen unexpectedly in simulations. The ratio between the total number of one ion species and that of another ion species, and the ratio between the flux of one ion species and that of another ion species do not depend significantly on the relative dielectric coefficient.

Regularization of Integral Operators in Singularly Perturbed Problems Using Normal Forms

Vestnik MEI ◽  
2019 ◽  
Vol 6 ◽  
pp. 131-137
Author(s):  
Abdukhafiz A. Bobodzhanova ◽  
◽  
Valeriy F. Safonov ◽  
Keyword(s):  
Normal Forms ◽  
Integral Operators ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problems

scholarly journals Dynamic of a nonautonomous two-species impulsive competitive system with infinite delays

2019 ◽  
Vol 17 (1) ◽  
pp. 776-794 ◽  
Author(s):  
Mengxin He ◽  
Zhong Li ◽  
Fengde Chen
Keyword(s):  
Comparison Theorem ◽  
Mathematical Analysis ◽  
Global Attractivity ◽  
Infinite Delay ◽  
Applied Mathematics ◽  
Almost Periodic ◽  
Competitive System ◽  
Dynamic Behaviors ◽  
Impulsive Equation ◽  
Infinite Delays

Abstract In this paper, we consider a nonautonomous two-species impulsive competitive system with infinite delays. By the impulsive comparison theorem and some mathematical analysis, we investigate the permanence, extinction and global attractivity of the system, as well as the influence of impulse perturbation on the dynamic behaviors of this system. For the logistic type impulsive equation with infinite delay, our results improve those of Xuxin Yang, Weibing Wang and Jianhua Shen [Permanence of a logistic type impulsive equation with infinite delay, Applied Mathematics Letters, 24(2011), 420-427]. For the corresponding nonautonomous two-species impulsive competitive system without delays, we discuss its permanence, extinction and global attractivity, which weaken and complement the results of Zhijun Liu and Qinglong Wang [An almost periodic competitive system subject to impulsive perturbations, Applied Mathematics and Computation, 231(2014), 377-385].

A Parameter Robust Finite Element Method for Fourth Order Singularly Perturbed Problems

2017 ◽  
Vol 17 (2) ◽  
pp. 337-349 ◽  
Author(s):  
Christos Xenophontos
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fourth Order ◽  
Hermite Polynomials ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
The Finite Element Method ◽  
Singularly Perturbed Problems ◽  
Exponentially Graded ◽  
Element Method

AbstractWe consider fourth order singularly perturbed problems in one-dimension and the approximation of their solution by the h version of the finite element method. In particular, we use piecewise Hermite polynomials of degree ${p\geq 3}$ defined on an exponentially graded mesh. We show that the method converges uniformly, with respect to the singular perturbation parameter, at the optimal rate when the error is measured in both the energy norm and a stronger, ‘balanced’ norm. Finally, we illustrate our theoretical findings through numerical computations, including a comparison with another scheme from the literature.

scholarly journals The human sperm beats anisotropically and asymmetrically in 3D

2019 ◽  
Author(s):  
Hermes Gadêlha ◽  
Paul Hernández-Herrera ◽  
Fernando Montoya ◽  
Alberto Darszon ◽  
Gabriel Corkidi
Keyword(s):  
Ion Channels ◽  
Mathematical Analysis ◽  
Molecular Motors ◽  
High Speed ◽  
3D Imaging ◽  
Human Sperm ◽  
Travelling Wave ◽  
Fundamental Question ◽  
Sperm Flagellum ◽  
Straight Line

The canonical beating of the human sperm flagellum is postulated to be symmetric. This is despite the reported asymmetries inherent to the flagellar axonemal structure, from distribution and activation of molecular motors to, even, the localisation of regulatory ion channels. This raises a fundamental question: how symmetric beating is possible within such intrinsically asymmetric flagellar complex? Here, we employ high-speed 3D imaging with mathematical analysis capable of resolving the flagellar movement in 4D (3D+time). This reveals that the human sperm beating is both anisotropic and asymmetric, and composed by a superposition of two transversal waves: an asymmetric travelling wave and a symmetric standing wave. This novel anisotropic travelling-pulsation mechanism induces sperm rolling self-organisation and causes a flagellar kinematic illusion, so that the beat appears to be symmetric if observed with 2D microscopy. The 3D beating anisotropy thus regularises the intrinsic flagellar asymmetry to achieve symmetric side-to-side movement and straight-line swimming.

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